Vollständige Lösung der unbestimmten GleichungX 3q+Y3=1 in ganzèn Zahlen

Ohne ZusammenfassungDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischerDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischerDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischerDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischerDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischer     

An analysis of setup cost reduction in a two stage system

This paper investigates the impact of investing in setup cost reduction in a two stage manufacturing process. Closed form relationships are developed for the cases of investment in primary stage setup cost reduction, investment in finishing stage setup cost reduction, and simultaneous investment in setup cost reduction in both stages. Numerical results are presented which compare each of the models to the basic model. These results indicate that when investment in both stages is feasible, it is most effective to simultaneously invest in setup cost reduction. Failing this, the next best alternative is to invest in setup cost reduction in the finishing stage.     

Asymptotic expansion of solutions in a rolling problem

Asymptotic methods in the theory of differential equations and in nonlinear mechanics are commonly used to improve perturbation theory in the small oscillation regime. However, in some problems of nonlinear dynamics, in particular for the Higgs equation in field theory, it is important to consider not only small oscillations but also the rolling regime. In this article we consider the Higgs equation and develop a hyperbolic analogue of the averaging method. We represent the solution in terms of elliptic functions and, using an expansion in hyperbolic functions, construct an approximate solution in the rolling regime. An estimate of accuracy of the asymptotic expansion in an arbitrary order is presented.     

The product representation theorem for interlaced pre-bilattices: some historical remarks

This note aims to unravel the history of the Product Representation Theorem for Interlaced Pre-bilattices. We will see that it has its lattice-theoretic roots in early attempts to solve one of the problems in Birkhoff’s Lattice Theory. The theorem was presented in its full generality by Czédli, Huhn and Szabó at a conference in Szeged, Hungary in 1980 (and published in 1983). This was several years before Ginsberg introduced bilattices at a conference on artificial intelligence in 1986 and in his foundational paper in 1988.     

Promoting number theory in high schools or birthday problem and number theory

The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges.     

The existence and uniqueness of<Emphasis Type="Italic">q</Emphasis>-process in random environment

We introduce some basic concepts such as random (sub-)transition function, q-function in random environment, g-process in random environment and some basic lemmas. For any continuous g-function in random environment, we prove that the g-process in random environment always exists, and that any g-process in random environment satisfies the random Kolmogorov backward equation and the minimal g-process in random environment always exists. When g is a continuous and conservative g-function in random environment, the necessary and sufficient conditions for the uniqueness of g-process in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous g-processes in random environments are considered.     

Supporting Statistics in the Workplace: Experiences with two Hospitals

This paper provides some rejections on the promotion of lifelong learning in statistics in the workplace. The initiative from which the rejections are drawn is a collaboration between a university and two public hospitals, of which one of the stated aims is to develop statistical skills among the hospitals' researchers. This is realized in the provision of 'biostatistical clinics' in which workplace teaching and learning of statistics takes place in one-on-one or small group situations. The central issue that is identified is the need to accommodate diversity: in backgrounds, motivations and learning needs of workplace learners (in this case medical researchers), in the workplace environments themselves and in the projects encountered. Operational issues for the statistician in providing such training are addressed. These considerations may reject the experiences of the wider community of statisticians involved in service provision within a larger organization.     

角蛋白16和17在部分表皮肿瘤中的表达和意义

目的 研究角蛋白16 和17（K16、K17）在部分表皮肿瘤中的表达和意义。方法 采用免疫组化法检测K16、K17在正常皮肤、脂溢性角化病、日光性角化病、皮角、基底细胞癌、鳞状细胞癌中的表达。结果 K16、K17 在正常皮肤表皮各层呈阴性表达;在脂溢性角化病表皮各层中除了角质层外大多呈阳性表达;在日光性角化病表皮K16 均不表达,K17 除了角质层外在其他各层也不表达;K16 在皮角表皮棘层呈强阳性表达,但在其他各层均呈阴性表达,K17 在皮角表皮各层基本呈阳性或强阳性表达;在基底细胞癌中,K16、K17除了在棘层呈弱阳性表达外,在其他各层均呈阴性表达;在鳞状细胞癌中,K16 在基底层呈阴性表达,但在其他各层及K17 在表皮全层均呈阳性或强阳性表达。K16 除基底层外在肿瘤表皮其他各层表达比较差异均有统计学意义（均P＜0.05）;K17 在表皮各层表达差异均有统计学意义（均P＜0.05）。结论 K16、K17的表达状况可为表皮肿瘤的鉴别诊断提供病理学方面的依据。     

The role of examples in forming and refuting generalizations

Acknowledging students’ difficulty in generalizing in general and expressing generality in particular, we assert that the choice of examples that learners are exposed to plays a crucial role in developing their ability to generalize. We share with the readers experiences in which examples supported generalization, and elucidate the strategies that worked for us in these circumstances, presuming that similar strategies could be helpful with other students in other settings. We further share several pitfalls and call for caution in avoiding them.     

Harmonic wavelets in boundary value problems for harmonic and biharmonic functions

We consider boundary value problems in a disk and in a ring for homogeneous equations with the Laplace operator of the first and second orders. Solutions are represented in terms of bases of harmonic wavelets in Hardy spaces of harmonic functions in a disk and in a ring, which were constructed earlier.     

Interpretations of National Curricula: the case of geometry in textbooks from England and Japan

This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13–14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks.     

Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan

This study examined (a) the differences in preservice teachers’ procedural knowledge in four areas of fraction operations in Taiwan and the United States, (b) the differences in preservice teachers’ conceptual knowledge in four areas of fraction operations in Taiwan and the United States, and (c) correlation in preservice teachers’ conceptual knowledge and procedural knowledge of fractions in Taiwan and the United States. Participants were preservice teachers (N = 49) in a teacher education program in the United States and comparable Chinese preservice teachers (N = 47). Results indicated that Chinese preservice teachers performed better in procedural knowledge on fraction operations than American preservice teachers. No significant differences were found for conceptual knowledge on fraction division. Further, the correlation in this study showed that for Chinese and American preservice teachers, the relationship between conceptual and procedural knowledge of fraction operations was weak.     

Rolling in the Higgs model and elliptic functions

Asymptotic methods in nonlinear dynamics such as, for example, the Krylov-Bogoliubov averaging method and the KAM theory are commonly used to improve perturbation theory results in the regime of small oscillations. But for a series of problems in nonlinear dynamics, in particular, for the Higgs equation in field theory, not only the small-oscillation regime but also the rolling regime is of interest. Both slow- and fast-rolling regimes are important in the Friedmann cosmology. We present an asymptotic method for solving the Higgs equation in the rolling regime. We show that to improve the perturbation theory in the rolling regime, expanding a solution known in terms of elliptic functions not in trigonometric functions (as with the averaging method in the small-oscillation regime) but in hyperbolic functions turns out to be effective. We estimate the accuracy of the second approximation. We also investigate the Higgs equation with damping.     

Preface

We are presenting in this volume the collection of extended abstracts of 66 talks that were presented at Combinatorics 2012 in Perugia, Italy. Combinatorics 2012 is the 17th in the series of combinatorics conferences held in Italy, first in 1981, next in 1982 and every two years since then.     

Leslie Fox

Leslie Fox was born in Yorkshire in 1918, and spent most ofhis professional life in Oxford, as Director of the UniversityComputing Laboratory and as the first Professor of NumericalAnalysis in the University. His mathematical education began at the Wheelwright GrammarSchool in Dewsbury, which produced a number of distinguishedmathematicians and scientists at about the same time as Foxunder the influence of an inspiring Headmaster and teacher (LeslieSadler). Fox went to Oxford in 1936 as a scholar of Christ Church,and he gained a First Class Honours degree in Mathematics. Hecontinued his studies for a DPhil under the direction of ProfessorSir Richard Southwell, with a project in the area of computationaland engineering mathematics which initiated some of the maininterests of his career. His first appointment was at the AdmiraltyComputing Service in 1943; here he learnt the skills of table-makingwhich he later used in a number of publications. In 1945 Fox and several colleagues moved to the new MathematicsDivision of the National Physical Laboratory. It was recognisedat that time that the emerging technology of automatic computationwould lead to requirements for effective mathematical methodswhich exploited the new machinery. The Mathematics Divisionembarked on an extensive programme of research in computationalmethods, in parallel with the construction of the Pilot ACEmachine, which carried out its first computations in 1950. TheDivision remained a major source of ideas and methods in numericalmathematics for many years, with Fox taking a leading role untilhe was appointed to set up the Computing Laboratory in Oxfordin 1957.     

政府花费改变对经济影响的理论分析

本文采用无限期内生时间偏好率模型,研究了政府花费对经济的影响.指出长期的政府花费增加可以使资本存量水平上升,消费水平下降和债券持有量上升;同时,短期分析表明政府花费增加可以减少初始投资率,增加政府债务率水平;但短期的政府花费增加同样导致资本存量水平上升,消费水平下降和债务水平的增加.     

Representations of Nature of Science in Selected Histories of Science in the Integrated Science Textbooks in China

This study aimed to examine the representations of nature of science (NOS) in the eight histories of science selected from three series of integrated science textbooks used in junior high school in China. Ten aspects of NOS were adopted in the analytical framework. It was found that NOS had not been well treated in the selected histories of science in the three series of science textbooks. Specifically, it was found that the empirical and inferential aspects were treated better than other aspects, and discrepancies existed among the three series of science textbooks and among the eight histories of science in terms of dealing with the target NOS aspects. Implications for addressing NOS in historical materials in science textbooks were discussed in the final part of this paper.     

Point Configurations in <Emphasis Type="Italic">d</Emphasis>-Space without Large Subsets in Convex Position

In this paper we give a lower bound for the Erd\H os–Szekeres number in higher dimensions. Namely, in two different ways we construct, for every $n>d\ge 2$, a configuration of $n$ points in general position in $\R^d$ containing at most $c_d(\log n)^{d-1}$ points in convex position. (Points in $\R^d$ are in convex position if none of them lies in the convex hull of the others.)